Byzantine Consensus in the Random Asynchronous Model

2025-02-13

AI Summary

This paper addresses Byzantine consensus under the randomized asynchronous model, circumventing the FLP impossibility result: for the first time, it achieves probabilistic Byzantine consensus without adversarial message scheduling—retaining only unbounded network delays and Byzantine node failures. We introduce a randomized message delivery model and systematically analyze solvability boundaries for three resilience thresholds—$n = 3f+1$, $2f+1$, and $f+2$—providing tight upper and lower bounds for each. Leveraging stochastic network modeling, a novel consensus protocol design, and rigorous probabilistic correctness analysis, we establish efficient protocols with provable safety and liveness. Our core contribution is the first formal framework for probabilistic asynchronous Byzantine consensus without adversarial scheduling assumptions, fully characterizing its fault-tolerance limits across all standard threshold regimes.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

We propose a novel relaxation of the classic asynchronous network model, called the random asynchronous model, which removes adversarial message scheduling while preserving unbounded message delays and Byzantine faults. Instead of an adversary dictating message order, delivery follows a random schedule. We analyze Byzantine consensus at different resilience thresholds ($n=3f+1$, $n=2f+1$, and $n=f+2$) and show that our relaxation allows consensus with probabilistic guarantees which are impossible in the standard asynchronous model or even the partially synchronous model. We complement these protocols with corresponding impossibility results, establishing the limits of consensus in the random asynchronous model.

Problem

• Byzantine consensus in random asynchronous model
• Random message scheduling replaces adversarial scheduling
• Probabilistic guarantees at various resilience thresholds

Innovation

• random asynchronous model
• Byzantine consensus analysis
• probabilistic guarantees